To go back to your original question Vern. The small gravitational fields involved in the rotation of galaxies produce an extremely small effect on time it is only when you get very close to the event horizon of a black hole that time dilation becomes significant.

The consensus seems to be that GR does take into account the affect that gravity has upon gravity. I still haven't seen the details of how this works. Simple arithmetic says it can't work. But GR ain't simple.

let's put it this way, for us to observe something as moving spatially one would expect energy to be involved somehow initially at least, so in that motto a gravity wave can be seen as needing 'energy'. But the wave we might see is like a bubble wandering inside a liquid, a local disturbance of a field, so I'm not that sure that gravity waves contain any 'energy' in themselves. Don't know how to express it really but the 'effect' we would observe is more due to the surrounding vacuum/densities adapting themselves than to the 'bubble' releasing some indefinable 'energy', it seems to me.

The consensus seems to be that GR does take into account the affect that gravity has upon gravity. I still haven't seen the details of how this works. Simple arithmetic says it can't work. But GR ain't simple.

How I've heard it described is because the energy and momentum of a body tells space-time how to curve, and the curvature tells the body how to move (and moving gives it energy and momentum, meaning it therefore influences the curvature).

What forbids a black hole is the fact that it is a singularity Vern, 'Terra Incognito'. You can't divide with zero, so in that motto we need some really 'phreaky math' to come up with ideas for what might be in there. Seems like it's only string theory that have succeed with that, as yet?

If they are right? Well, as far as I know it's still a purely mathematical construction, without any real experimental evidence, but that might change, and maybe there is the possibility of indirect evidence too? Like things we can't really observe but still have good reasons to expect to exist, like vacuum energy.

I suspect the answer will not come through string theory. When I look at Poincare's work, I get the feeling that he knew the answer to the final puzzle. The answer wasn't acceptable in his time. It's still not.

The equation for acceleration contains time as an element. Stars in galaxies experience acceleration toward the galactic centre. Massive objects in a gravity field experience the passage of time as being slower than if the gravity field were not there.

So it seems that gravity would have a negative affect upon gravity so that it would not follow a linear increase as mass increases.

Time dilation due to gravity should then be considered when calculating the expected speed of galactic rotation.

What am I missing?

The bigger the galaxy the more the space rotates with the galaxy.

No centrifugal force is generated when you rotate at the same rate that the space rotates.

No centrifugal force is generated when you rotate at the same rate that the space rotates.

I wonder could it really be so that there's no centrifugal force?

Now let's shoot a relativistic projectile at a small black hole.

After the shot the black hole is moving backwards.

A pushing force between the projectile and the black hole caused the backwards motion.

A pushing gravitational force.

Also when dropping something into a black hole there is a pushing force. First there is a pulling force, then there is a pushing force. That's why the black hole does not change its speed when an object is dropped into it.